QUESTION 8 The manager of a seafood restaurant was asked to establish a pricing

ID: 423632 • Letter: Q

Question

QUESTION 8 The manager of a seafood restaurant was asked to establish a pricing policy on lobster dinners. The predict the lobster sales on each day. The pertinent historical data are collected as showa in the table. Anaswer the following que manager intends to use the pricing S/ILB to Day Lobster Price ($lb.) 195 190 188 179 170 162 7161 7.9 6.0 6.4 6.8 2 7.6 a) x - independent variable. According to this problem, the Ix b) r is the coeefficient of correlation. Use the r equation to compute the value of the denominator part of the equation. The value for the r denominator - (in 4 decimal places) in 4 c) According to this problem, the correlation of coefficient, r, between the two most pertineat variables is - decimal places) d) According to the instructor's lecture, the correlation strength between any two variables can be described as strong, weak or no corelation. The correlation strength for this problem can be described as e) According to the instructor's lecture, the correlation direction between any two variables can be described as direct or indicest relationship. The correlation direction for this problem can be described as relationship f) Regardless, you were told to use the Associative Forecasting method to predict the expected lobster sale. If the lobster price - $8.58, the expected #s of lobster sold (round to the next whole #).

Explanation / Answer

The calculation is as shown in following table:

Sr. No.

Price ($/lb.)

Lobster Sold/day

x*y

x*x

y*y

195

1170

38025

6.4

190

1216

36100

6.8

188

1278

35344

179

1253

32041

7.1

170

1207

28900

162

1231

26244

161

1272

25921

Total

= 48.80

= 1245.00

?xy

= 8627.50

?x2

= 342.78

?y2

= 222575

Mean

x-bar

= 6.97

y-bar

= 177.86

Price of the lobster is used for predicting the sales of lobsters, thus sales depends on price.

x = independent variable = price of lobster, ?x = 48.80

r = [ (n(?xy) - {(?x)(?y)} ] / Square Root {[ n(?x2) - (?x)2 ]*[ n(?y2) - (?y)2]}

Denominator = Square Root {[7(342.78) - (48.80)2 ]*[7(222575) - (1245)2]} = 379.684

Denominator = 379.6841

r = [(7*8627.5) – (48.80)(1245)]/379.6841 = - 363.5/379.6841 = -0.9574

r = - 0.9574

When r = 0, there is no correlation between variables

When, r value is near to 1 or -1, the relation is strong.

When r value is less than 0.9 the relation is said to be weak.

Since, the calculated r value is near to 1, the relationship is strong.

Ans: Strong.

If the r value is greater than zero it is direct correlation and when less than zero, it is indirect correlation.

Since r value is less than zero, the correlation is indirect.

If the price reduces the sale increases and vice-versa.

ANS: Indirect

The associate forecasting method is linear regression method between to variables which is given by following equation:

Y = a + bx

Calculate the Slope (b) and the Intercept (a) of the above data as follows:

b = [ n(?xy) - {(?x) (?y)} ] / [n(?x2) - (?x)2]

b = [(7)(8627.50) - (48.80)(1245)] / [(7)(342.78) - (48.80)2]

b = -20.1720

a = (y-bar) – (b)(x-bar)

a = (177.86) – (-20.1720)(6.97)

a = 318.4850

Part Four: Fill in the Slope and Intercept values for the Linear Regression equation below: